If
you come across (or have written) something interesting, please don't
hesitate to email it over: marketfolly (at) gmail (dot) com. Today
we'll post the first installment of the 'analytical links' and tomorrow
will feature the 'hedge fund links.' Enjoy!

Value investor Mohnish Pabrai sat down for an interview with The Motley Fool to talk about his approach and how he uses checklists in his investment process.

Checklist Investing & Learning From Mistakes

Pabrai had an epiphany after learning from concepts discussed in Atul Gawande's book The Checklist Manifesto. Essentially, he tries to learn from his mistakes by figuring out what went wrong with certain investments and how he could have prevented losses/a specific outcome.

But he also looked at some of the best investors in the world and incorporated their mistakes as well (looking at Warren Buffett, Charlie Munger, LongLeaf Partners, Third Avenue, etc).

Pabrai's Investment Checklist

Pabrai says that, "And what was stunning to me is that in almost all cases where I could figure out the reason for the loss, it was very apparent before the investment was made, number one. And the second is the reason was very basic. It wasn't some esoteric reason that you had to do some higher math to the fifth decimal to figure out this wasn't going to work. It was very basic."

While Pabrai has never revealed his checklist, he notes that there's about 98 questions on it that examines before making an investment. He does drop a few hints as to what he looks for though:

"So for example, we have a set of questions which relate to leverage. Debt covenants, how levered and all kinds of different issues related to leverage, because that has caused a lot of investments to go south. We have another set which relates to moats, the lack thereof, right? And so all kinds of things. There's another set of questions which relate to things like unions and labor relations. There's another whole set of questions on management and ownership. Just all kinds of nuances of whether they own stock, do they act like owners and all those sorts of things that come up. And then there are a few miscellaneous ones."

Since applying the checklist, Pabrai feels that his investment error rate has dropped significantly. Embedded below is the video of Pabrai's interview on checklist investing:

Leon Cooperman’s hedge fund, Omega Advisors, has disclosed a new position in London listed Monitise (LON: MONI). Due to trading on January 10th, Omega Advisors now holds 5.65% of Monitise’s voting rights.

Per Google Finance – “Monitise plc is a United Kingdom-based holding company. The principal activity of the Company is as a technology company delivering mobile banking, payments and commerce networks worldwide. The Company’s segments include Live Operations, Investment in future operations and Investment in technology platform. Live operations include both territory deployments and development contracts, which consist of Monitise United Kingdom, Monitise Americas and Global accounts. Investment in future operations segment represents the Company’s operations which are not live operations covering both pre-sales and start-up period. Investment in technology platform segment comprises the ongoing development, enhancement and maintenance costs of the Monitise technology platform.”

Wednesday, January 16, 2013

Investing is a continual education and from time to time we like to highlight concepts on refining investment process. Today we present a piece on position sizing utilizing the Kelly Growth Criterion.

The following is a guest post from Kyle Mowery, who founded GrizzlyRock Capital in 2011 as a long / short manager investing in corporate debt and equity securities. He can be reached at kyle@grizzlyrockcapital.com or at www.grizzlyrockcapital.com.

Position Sizing Utilizing the Kelly Growth Criterion

One of the more vexing tasks for investment allocators is position sizing. Regardless whether allocators select investment managers or individual securities, optimal position sizing is paramount to portfolio success. Small allocations to prescient investments minimize their impact while large allocations to poorly performing investments leads to underperformance.

Some allocators elect to equal-weight investments given uncertainty regarding which investments will perform best. This strategy creates a basket of attractive investments that should profit regardless of which investments in the basket succeed. This method benefits from simplicity and recognizes the future is inherently uncertain. Drawbacks of the strategy include underweighting exceptional investments and overweighting marginal ideas.

Another strategy is to allocate large amounts of capital to the investment ideas with the most potential. This methodology suggests investors should invest proportionally according to their ex-ante return expectations. The advantage of this methodology is matching prospective return to investment size. However, this strategy breaks down when allocators are incorrect about future investment return or risk prospects.

Investment allocators determine their methodology through a combination of portfolio mandate, risk tolerance, and confidence level in investment assessments. While the various approaches implemented are directionally helpful, most are mathematically sub-optimal. There is a better way - the Kelly Growth Criterion.

Kelly Growth Criterion

The Kelly Growth Criterion is a simple formula that determines mathematically optimal allocations to maximize long-term portfolio performance given each investment’s probability of success (“edge”) compared to the amount gained or lost (“odds”). The formula assumes a bimodal outcome of success (“base case”) or failure (“stress case”) over a single time period:

(click to enlarge)

The formula’s power lies in considering both the chance of success and payoff offered. For example the formula would urge a large investment if you had a significant edge given reasonable odds or exceptional odds payoff offsetting a moderate chance of success.

Ok, How Can the Formula be Applied to Investing?

When applied to investing, the Kelly Growth Criterion formula has six inputs. First is simply portfolio size. Second is the amount of capital the portfolio will risk in the pursuit of gain. This amount is also called the maximum tolerable drawdown. For a venture capital group this number will be high while a conservative pension plan would be willing to risk much less. Portfolio size and maximum tolerable drawdown remain constant for each portfolio analyzed regardless of specific investment opportunities.

Next comes four factors regarding the investment itself: the probability of gain in a base case, probability of loss in a stress case, percent of projected gain in the base case, and percent of projected loss in the stress case. The formula is below:

(click to enlarge)

For example, let’s say we are running a $100 million portfolio of US equities. Our mandate is fairly conservative so let’s assume the maximum portfolio drawdown tolerable to be 15% of assets.

We believe General Electric is attractive but are not sure how to size the position within our portfolio. Our team has agreed that our projected gain in the base case is 12% while we would lose 8% in the stress case. Further, the team has agreed the probability of gain to be 55% (base case) and a 45% probability of loss (stress case). Ok, so how much capital do we allocate to General Electric stock?

(click to enlarge)

Given both a strong “edge” (55% probability of success) and advantageous “odds” (12% projected gain in the base case is greater than 8% projected loss in the stress case), the formula suggests we allocate 3.75% of our portfolio to GE. If the “edge” was even, the formula would recommend a 2.50% allocation – again due to the disproportionate odds of success (12% vs. 8%).

What strikes many allocators initially is the magnitude of the size. Is 3.75% really optimal under a scenario with only a 55% probability of success? Mathematically speaking, yes. Why does this seem high?

The recommended 3.75% investment in GE seems high due to the commonality of diversification by funds and investment allocators. Let’s again work an example with our $100 million fund with a 15% maximum tolerable drawdown. Let’s further assume this fund has 100 investments therefore averaging 1.0% per investment. If an allocator takes the view that the “edge” is a coin flip (i.e. probability of success is equal to probability of failure). What would an allocation of 1.00% imply about the expected “odds”?

(click to enlarge)

As shown above, a 1.00% allocation to a position implies just an 11.54% gain in the base case versus a 10.00% decline in the stress case assuming equal odds. These odds are hardly the makings of a scintillating investment.

Why is the Kelly Growth Criterion Rarely Used for Investment Allocation?

Given the formula is mathematically optimal and simple to implement, one might think allocators would embrace the tool. However, investment allocators are not aware of this tool primarily because academic finance has not fully embraced the tool. Secondly, there are a few key weaknesses of the tool.

How Can Inherent Limitations of the Kelly Growth Criterion Formula be Overcome by Investment Allocators?

(1) Ex-ante input assumptions are inherently precise: As with any model, the formula is only as good as its inputs. How can allocators know beforehand whether an investment has a 50% or 55% chance of success? This input must be estimated without an ability to determine the efficacy of the estimate ex-post facto.

The simplicity and power of the formula is a double-edged sword. If investment allocators systematically overestimate the probability of success, long run return will be hampered. The offset of this risk is to estimate projected gains and success probability conservatively. If allocators error on the conservative side, the model will allocate smaller amounts to each investment. This is perfectly acceptable given the model’s proclivity to encourage substantial position sizes.

(2) The formula cannot account for correlation: The Kelly Growth Criterion accounts for an investment’s specific edge and odds. As such, the formula cannot address the relationship between portfolio investments and thus does not account for correlation.

Ask anyone who invested during 2008, correlations rise during a stress environment. If the probabilities of investment success (“edge”) in a given portfolio are correlated, a portfolio allocated strictly according to the Kelly Growth Criterion would be susceptible to risk factors which increase correlation.

There are two mitigants for this risk: (1) Invest in securities with divergent risk factors. If your edge in each investment is not correlated, the formula will provide a strong outcome at a portfolio level. (2) Akin to the mitigants for imprecise input assumptions, estimating a conservative edge and odds for each investment will decrease position sizing in any one security. By avoiding the weaknesses of the Kelly Growth Criterion, the robustness of the formula is enhanced.

(3) The formula assumes a single time period while portfolios are managed more frequently: The Kelly formula assumes a bimodal outcome, success or failure. Portfolio managers often confront prices that meander towards their eventual outcome over time. As prices change, positions sizing will be suboptimal at various times. To compensate for the model’s simplicity, allocators should specify time horizons before entering a position. For example, if hiring a private equity fund manager with an investment horizon of 10 years your Kelly Growth formula will utilize a much longer time frame than if you manage a trading book.

My firm, GrizzlyRock Capital, utilizes long-term, fundamental value methodology. As such, we utilize a period of multiple years when applying the Kelly Growth Criterion. We calculate the value of a business using an upside, base, and stress case and then utilize the base and stress case forecast in the Kelly formula. This conservatism allows the investment to trend towards our base case without our needing to reassess position sizing using the formula.

Conclusion

The Kelly Growth Criterion is valuable to investment allocators given the systematic, repeatable process and mathematically optimal portfolio structure. While a practical tool, the formula is not a silver bullet. When used conservatively, the formula will maximize portfolio growth by allocating capital to the most advantageous investments given both prospective return and risk.

Bill Miller of Legg Mason and Ed Thorp of Princeton Newport Partners (now closed) are investors with stellar track records over decades who embrace and advocate the use of the Kelly Growth Criterion in portfolio allocation. In his recent treatise, Antifragile, Nassim Taleb lavishes praise on the Kelly Growth Criterion: “Kelly’s method requires no joint distribution or utility function. In practice one needs the ratio of expected profit to worst-case return – dynamically adjusted to avoid ruin.”

At GrizzlyRock, we have found utilizing the Kelly formula eliminates our emotional biases towards certain aspects of investing and provides a stable, repeatable investment allocation of capital. Please drop me a line at kyle@grizzlyrockcapital.com if you wish to discuss further or be added to our distribution list.

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